E602: “Does every almost-disjoint countably infinite family with no singleton intersections have Property B?”

Open

Statement	User	Model	Harness	Time
1)V1Given a family of countably infinite sets whose distinct members intersect finitely but never in exactly one…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

1) V1 Given a family of countably infinite sets whose distinct members intersect finitely but never in exactly one point, is there a two-coloring under which no member is monochromatic?

open, filed Tue Aug 25 2026 04:32:54 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The coloring is defined on the whole ambient type rather than only the union; restriction and arbitrary extension make these formulations equivalent.

Scope. Arbitrary ground and index types, countably infinite family members, finite pairwise intersections excluding cardinality one.